- Identify the given acceleration as \(32 \text{ ft/s}^2\).
- Recall the unit conversion factor: \(1 \text{ foot} = 12 \text{ inches}\).
- Multiply the value by the conversion factor: \(32 \times 12 = 384 \text{ in/s}^2\).
- Match the result to the correct option, which is \(\boxed{384}\).
Explanation
- Analysis of the Problem
The acceleration due to gravity is given as \(32 \text{ feet per second squared}\). Our objective is to determine this acceleration in units of \(\text{inches per second squared}\). This is a unit conversion problem that requires the standard conversion factor between feet and inches.
- Performing the Conversion
We know that one foot is equivalent to twelve inches:
\[1 \text{ foot} = 12 \text{ inches}\]
To convert an acceleration value from \(\text{ft/s}^2\) to \(\text{in/s}^2\), we multiply the value in feet by the number of inches in a single foot.
Given the acceleration \(a = 32 \text{ ft/s}^2\), we perform the calculation:
\[a_{\text{in/s}^2} = 32 \frac{\text{ft}}{\text{s}^2} \times 12 \frac{\text{in}}{\text{ft}} = 384 \frac{\text{in}}{\text{s}^2}\]
Thus, the acceleration due to gravity is \(384 \text{ inches per second squared}\).
- Conclusion
Comparing our result of \(384\) \(\text{in/s}^2\) with the given options:
A\(\frac{3}{8}\) inches per second squared
B\(2 \frac{2}{3}\) inches per second squared
C\(384\) inches per second squared
D\(1,024\) inches per second squared
The calculated value matches option (c). Therefore, the final answer is \(\boxed{384}\).
Examples
Understanding unit conversion is fundamental in various fields, such as engineering, physics, and construction. For example, if an architect specifies a beam length in feet but the steel manufacturer works in inches, the architect must convert the measurements to ensure the materials are fabricated correctly. Similarly, in physics, keeping track of units ensures that calculations are consistent and meaningful across different systems of measurement. This simple multiplication principle is a building block for more complex dimensional analysis in scientific research.